Question

In three- dimensional space, the equation $3y+4z=0$ represents

• A. a plane containing x- axis
• B. a plane containing y- axis
• C. a plane containing z- axis
• D. a line with direction ratios $0,3,4$

Answer 1

The correct option is A a plane containing x- axis

The equations: $ax+by+cz+d=0$ is the equation of a plane. Therefore, the last option is incorrect.
Any point on the x-axis is of the form: $(h,0,0)$
It can be seen that the above point satisfies the equation $3y+4z=0$ for all $h$.
Therefore, the above plane contains the x-axis.
Any point on the y-axis is of the form: $(0,l,0)$
It can be seen that the above point does not satisy the equation $3y+4z=0$ for all $l$.
Therefore, the above plane does not contain the y-axis.
Similarly, it can be seen that it does not contain the z-axis either.